Floating-point numbers with error estimates

Masotti, Glauco

doi:10.1016/0010-4485(93)90069-z

Cited by 7 publications

(4 citation statements)

References 18 publications

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“…Other real-time techniques attempt to mitigate error, but only do so by increasing the overhead. Some of these techniques have the goal of computing results within error bounds, such as interval arithmetic [30] and real-time statistical analysis [31], [32]. But these require two floating point operations and require the storage of two floating point values and, thereby, increase the needed time and memory.…”

Section: Other Mitigation Techniquesmentioning

confidence: 99%

Bounded Floating Point: Identifying and Revealing Floating-Point Error

Jorgensen¹,

Vegas²,

Masters³

et al. 2021

Adv. sci. technol. eng. syst. j.

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This paper presents a new floating-point technology: Bounded Floating Point (BFP) that constrains inexact floating-point values by adding a new field to the standard floating point data structure. This BFP extension to standard floating point identifies the number of significant bits of the representation of an infinitely accurate real value, which standard floating point cannot. The infinitely accurate real value of the calculated result is bounded between a lower bound and an upper bound. Presented herein are multiple demonstrations of the BFP software model, which identifies the number of significant bits remaining after a calculation and displays only the number of significant decimal digits. These show that BFP can be used to pinpoint failure points. This paper analyzes the thin triangle area algorithm presented by Kahan and compares it to an earlier algorithm by Heron. BFP is also used to demonstrate zero detection and to correctly identify an otherwise unstable matrix.

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Section: Other Mitigation Techniquesmentioning

confidence: 99%

Bounded Floating Point: Identifying and Revealing Floating-Point Error

Jorgensen¹,

Vegas²,

Masters³

et al. 2021

Adv. sci. technol. eng. syst. j.

View full text Add to dashboard Cite

show abstract

“…As the addition of two floating-point numbers can be represented by a sum and an error, the multiplication between two floating-point numbers also has such a property, which means that the exact value of the product of two floating-point numbers can be represented by a sum of two floating-point numbers [12]. Priest [15] introduces a compound representation for floating-point numbers, called expansions, to reduce the rounding error and compute an accurate error.…”

Section: Outputmentioning

confidence: 99%

Line Segment Intersection Testing

2005

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“…If b does not have representation error, then b = 0, whence p = 0 and q = 0. Since the exact value of the product of two floating-point numbers can be represented by a sum of two floating-point numbers[9,10], ab could be exactly computed by ab = c + d, where c and d are two floating-point numbers. The minimal intervals that contain the value of AB are:…”

mentioning

confidence: 99%

Computing the Sign of a Dot Product Sum

Zhu

Yong

Zheng

2004

Computational and Information Science

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A real number usually cannot be exactly represented by a floating-point number in a computer. Namely, a floating-point number frequently stands for any real number in a specific interval. In this paper, we present a method for computing the sign of a dot product sum. Each initial datum that is a floating-point number is considered as an interval. With interval analysis and floating-point summation methods, an explicit formula for calculating the minimal interval of a dot product sum is presented. Error analysis and some examples are provided as well.

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Floating-point numbers with error estimates

Cited by 7 publications

References 18 publications

Bounded Floating Point: Identifying and Revealing Floating-Point Error

Bounded Floating Point: Identifying and Revealing Floating-Point Error

Line Segment Intersection Testing

Computing the Sign of a Dot Product Sum

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